[petsc-users] Ambiguity of KSPCGNE

[Alexander Grayver]

Hello,

I'm a bit confused about the KSPCGNE. First of all, is CGLS^1 and 
implemented CGNE are the same (or I mix it up with CGNR)? I don't know 
what notation is more classical, but CGLS seems to be more common.
It is claimed:

*/Applies the preconditioned conjugate gradient method to the normal 
equations without explicitly forming A^t*A /*

Does that mean I have to provide A to KSP? In this case the application 
of the method is quite restricted since all practical least squares 
problems formulated in form of normal equations are solved with 
regularization, e.g.:

(A'A + \lamba I)x = A'b

Assume I have A computed and use matrix free approach to represent (A'A 
+ \lamba I) without ever forming it, so what should I do then to apply 
KSPCGNE?

Thanks.

1. Bjorck, A., 1996. Numerical Methods for Least Squares Problems, p. 288

-- 
Regards,
Alexander

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